Ok, I've read through the entire thread while badly hungover...
Draka: I believe I understand where you're coming from. If one worships Loki one is a Norse Pagan, If one worships Hades one is a Greek Pagan. Why then is one who worships Satan not Abrahamic?
I believe I said in the other thread that those few Satanists who worship the biblical Satan could possibly be called Abrahamic. I also have a plethora of material covering why Neo-Satanists are not themselves Abrahamic, but I'll try to steer clear of that for this thread
Ok, I'm actually on the fence about calling the Satanists Draka is referring to as Abrahamic, so I'll try to look at a few reasons for and against using the term to describe them. Firstly, I think the strongest argument for calling them Abrahamic is the one Draka already presented. If they worship an entity from the Abrahamic pantheon, why should they not then be considered Abrahmic themselves? At the very least they could be described as being heretical Abrahamics from this argument.
One of the main problems with this argument though is it's largely hypothetical. Neo-Satanists, Luciferians, Setians, Demonolaters and Laveyan Satanists are our representatives of the "Satanic religions" in the West at least and none of them follow the checklist for the hypothetical "Abrahamic Satanist". Furthermore if we look at some of the historical examples of Satanism, we find that not only is it wrapped up in medieval propaganda making it very difficult to glean untarnished facts, but also those few medieval magicians who would call on the aid of Satan and his Demons would do so in the name of God.
In fact, not only was the name of God invoked during medieval demonomancy, but there is a strong emphasis on purity on behalf of the practitioner, "At once, the angel of the Lord appeared to him and said, 'Do not be amazed that the secrets of Solomon have remained hidden, for the Lord intended that this science would never fall into the hands of the wicked and the impure.'" p.4,
Grimorium Verum, Trans Joseph H. Peterson, 2007
So this is perhaps our best example of "Satanic" practices before the 20th century and this form of magic most certainly falls within Abrahamic tradition (though it may well be considered heretical). However, Satan and his demons are not worshipped or even respected in this context, instead they are forced to appear and bent to the magician's will. Grimorium Verum and the goetic tradition is riddled with warnings against flaws in the rituals and the dangers the spirits present to the magician if not properly called upon and controlled. To me, this places it outside the sphere of Satanism.
Another problem is that rightly or wrongly, Abrahamic faiths have a different attitude to their pantheon than many other religions. It's very much a "you're in or you're out" attitude in some respects insofar as most definitions of "Abrahamic" I've come across require as a minimum the worship of the Abrahamic God and percieve Abraham himself as a spiritual father. Voodoo for example is generally not considered Abrahamic due to it's syncretism, despite actually making full use of the Christian pantheon. At the end of the day, perhaps because of the prevalence of Abrahamic faiths, the title just doesn't really extend to everybody who might use their pantheon.
Of course Devil worshippers have existed in one form or another around the world for millennia. While I'm not particularly knowledgeable about Zoroastrianism, there are some fantastic stories involving followers of Ahriman who were typically evil sorcerers who debased the Zoroastrian religion.
Now, as far as my own beliefs are concerned I would say that there is a Devil who pops up around the world throughout time in different forms and guises. While I'm a polytheist myself, I do believe in the Devil as this adversarial being and that regardless of the name or appearance given to it, it's largely the same spirit. In this sense I would suggest that even the hypothetical Satanist of the OP would fall outside the Abrahamic tradition insofar as their God spans across many religions and times. Of course, that's my own take on the matter.
I didn't want to have to fall back onto saying "It depends how you define Abrahamic" but I'm going to have to. I've been browsing various thoughts on this topic on the internet as well as refering to my own books while writing this post and I can see the arguments for both sides, but remain to be entirely convinced by either. :sorry1: